Will a 12.5 Kw generator supply enough electricity to power an average house?
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Yes, with qualifications.
If the house loads don't total more than about 50 amps from either leg of the supply, you should be OK. You should be able to pull about 50 amps @ 240 volts from the generator. From a purely mathematical view, that would be 100 amps @ 120v, but to get the full 100 amps, they have to be evenly distributed between the two legs of the supply. Check the breaker on the generator - it will probably be a 50 or 60 amp double pole, common trip breaker. That sets the absolute maximum that can be drawn from either leg of the supply.
Look at the circuits you plan to use on backup power, determine which are likely to be used simultaneously and what their expected current requirements will be - not necessarily the same as the breaker rating - and, if needed, move breakers around so that the simultaneous 120v requirements are evenly split between the two legs of the generator supply.
Unless there are simultaneous heating (range, water heater, furnace, etc), air conditioning, or large motor loads involved, 12.5 KW should be more than adequate for the necessary and critical loads. 240v loads draw equally from each leg so they don't have to be considered in the load-balancing exercise, but they do have to be considered in the total/simultaneous load determination.
